This project focuses on developing new statistical methods, and applying new and existing statistical techniques, to analyze data from laboratory animal studies. In particular, special emphasis is placed on the type of data arising in the National Toxicology Program (NTP) carcinogenesis bioassays. With respect to my own research time on this project, much of it is spent working on new solutions to problems viewed as important by NTP scientists. In addition, some of my research time is devoted to applying these new procedures to the data which originally motivated the work on methods development. Finally, the remainder of my research time is spent applying existing statistical procedures, sometimes in novel ways, to data collected by collaborators here at the National Institute of Environmental Health Sciences (NIEHS). Some of my methodological research is summarized in Dr. Shyamal Peddada's project entitled 'Statistical Theory and Methodology With Applications to Toxicology' (Z01-ES-101744) and some of my collaborative research is summarized in Dr. Peddada's project entitled 'NIEHS Statistical Consulting Service' (Z01-ES-045005). Otherwise, the rest of my research, as well as some of Dr. David Dunson's research, relate primarily to the development of new methods in two areas: (1) analysis of shape-constrained hazard functions and (2) accounting for body weight in causal inferences about tumor incidence. Both methods are developed in a Bayesian framework and use Markov Chain Monte Carlo (MCMC) computational techniques. These two areas of research are described in more detail below.